For example, from DE 100 02 455 A1 a stabilizer arrangement for the chassis of a motor vehicle has been known, in which an actuator is arranged between stabilizer halves, rotating the two stabilizer halves in reference to one another around a rotational axis, if necessary. Here, the rotation of the two stabilizer halves in reference to one another is to counteract the roll of the body. The actuator is provided with curved path carriers having one curved path each, in which a coupling element, that can be displaced, is guided along said curved paths by means of an actuating drive. For example, a ball screw can be provided as an actuating drive having a spindle nut arranged on its threaded spindle carrying the coupling element. The coupling element comprises pins, arranged laterally in reference to the rotational axis of the actuator, with support rolls being pivotally supported on them. These support rolls engage the curved paths of the two curved path carriers. With the rotation of the threaded spindle, the spindle nut shifts along the rotational axis of the actuator, with the support rolls rolling along the curved paths. During this adjustment motion, a relative rotation of the two curved path carriers occurs in reference to one another due to the design of the curved paths. This relative rotation creates a torque in the opposite direction of the undesired roll. One of the curved paths is embodied approximately S-shaped, with one end of the S-shaped curved path facing one axial end of the actuator and the other end of the S-shaped curved path facing the other axial end of the actuator. Seen in the longitudinal direction of the actuator, a neutral position or starting position of the actuator is located approximately in the middle of the S-shaped curved path. The displacement of the coupling element out of this starting position occurs, depending on the rolling direction, towards one axial end of the S-shaped curved path or towards the other one. In order to allow the construction space of the actuator to be reduced in the axial direction, the two curved path carriers may be arranged coaxially nested. It would be desirable to provide an anti-roll bar in which the axial construction space required is further reduced.